Topology-Preserving Multifractal Exchange Upscaling for Flow and Reactive Transport in Fractured Crystalline Rock

Qingjun Bao

Groundwater flow and radionuclide transport in fractured crystalline rock are governed by multiscale fracture connectivity, heterogeneous hydraulic properties, matrix diffusion, and coupled geochemical processes. Conventional continuum and discrete-fracture models often have difficulty preserving both geometric complexity and transport-relevant connectivity during upscaling. This study presents a topological–multifractal modeling framework that integrates discrete fracture-network representations, multifractal characterization, topological data analysis, graph-based transport descriptors, and hydrogeological upscaling. The framework is designed to characterize preferential flow paths, fracture–matrix exchange, reactive transport, and radionuclide migration across multiple spatial scales. The Revell Batholith in northwestern Ontario, Canada, is used as a geological validation context. The study establishes the mathematical formulation, computational workflow, and validation gates required to evaluate whether topological and multifractal descriptors can improve transport-relevant parameterization in fractured crystalline rock. The results provide a reproducible theoretical basis for future site-calibrated simulations and uncertainty analysis in groundwater assessment and deep geological repository research.